Game Development Reference
In-Depth Information
Skin Friction Drag
Skin friction drag is caused by the contact between the water and the hull as the hull slides
through the water. The water clings to the hull and resists the hull motion. Skin friction drag is
the dominant hydrodynamic drag component at lower boat velocities and is still significant at
higher velocities. The skin friction coefficient,
C
f
, is a function of the Reynolds number of the
boat. Recall from Chapter 5 that the Reynolds number is a nondimensional ratio of fluid density,
velocity, and a characteristic length,
L
, divided by the viscosity of the fluid,
m
.
r
vL
Re
=
(9.19)
m
The length term,
L
, in Equation (9.19) is generally taken to be either the length of the boat
or the length of the waterline (the line where the hull meets the water). The viscosity of fresh
and salt water is a function of temperature, and values for some typical water temperatures are
shown in Table 9-2. For game programming purposes, assuming the viscosity is a constant
0.001
kg/(m-s)
is probably a reasonable approximation.
Table 9-2.
Viscosity of Fresh Water and Seawater,
kg/(m-s)
r t re (
o
C
)
Temperature (
o
F
)
Temperature (
K
)
Viscosity,
Fresh Water
Viscosity,
Seawater
283
10
50
1.304e - 3
1.400e - 3
288
15
60
1.122e - 3
1.210e - 3
294
21
70
0.974e - 3
1.060e - 3
300
27
80
0.858e - 3
0.920e - 3
Several equations and techniques have been developed over the years to estimate the skin
friction coefficient. In 1957, the International Towing Tank Conference (ITTC) came up with an
equation that is still commonly used today.
1
0.075
C
=
(9.20)
f
(
)
2
log
Re
−
2
10
As an example of computing the skin friction coefficient, consider a boat traveling through
salt water at 10
m/s
. The temperature of the water is 283
K
, and the length of the waterline
of the boat is 8
m
. The Reynolds number based on waterline length can be computed from
Equation (9.19).
1025*10 *8
Re
=
=
5.86
e
+
7
(9.21)
0.0014
The skin friction coefficient based on this Reynolds number can be computed from
Equation (9.20).
